If $P\left( n \right):2 + 4 + 6 \ldots + \left( {2n} \right),\;n \in N,$ then $\begin{array}{l} P\left( k \right) = k\left( {k + 1} \right) + 2{\rm{implies}}\\ P\left( k \right) = \left( {k + 1} \right)\left( {k + 2} \right) + 2 \end{array}$ is true for all $k \in N.$ So, statement $P\left( n \right) = n\left( {n + 1} \right) + 2$ is true for

JEE MATHEMATICS MCQ: MATHEMATICAL INDUCTION

1 Easy

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Analyzing +4 | -1

P\left( n \right):2 + 4 + 6 \ldots + \left( {2n} \right),\;n \in N,

then

\begin{array}{l} P\left( k \right) = k\left( {k + 1} \right) + 2\mathrm{implies}\\ P\left( k \right) = \left( {k + 1} \right)\left( {k + 2} \right) + 2 \end{array}

is true for all

k \in N.

So, statement

P\left( n \right) = n\left( {n + 1} \right) + 2

is true for

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the base case

P(1)

is not true, meaning mathematical induction cannot be applied.